Ways of mounting optical elements within annular mounting rings and ways of stacking the rings to assemble a lens having a plurality of precisely mounted elements are explained in the parent application. This invention involves improvements in the annuli used in such a mounting system. It recognizes and provides a solution for a source of error occurring in the annuli as originally conceived and, by reducing such error, makes annulus mounted optical elements more accurate and improves the precision of lenses assembled by stacked annuli.